This chapter is from the book

Theoretical Roots: Determinants of PE Ratio

Investors have always used earnings multiples to judge investments. The simplicity and intuitive appeal of the price-earnings
(PE) ratio makes it an attractive choice in applications ranging from pricing initial public offerings to making judgments on
investments, but the PE ratio is related to a firm's fundamentals. As you will see in this section, a low PE ratio by itself does not indicate an undervalued stock.

What Is the PE Ratio?

The price-earnings ratio is the ratio obtained by dividing the market price per share by the earnings per share over a period.

The PE ratio is usually estimated with the current price per share in the numerator and the earnings per share in the denominator.

The biggest problem with PE ratios is the variations on earnings per share used in computing the multiple. The most common measure of the PE ratio divides the current price by the earnings per share in the most recent financial year; this yields the currentPE. Other people prefer to compute a more updated measure of earnings per share by adding up the earnings per share in each
of the last four quarters and dividing the price by this measure of earnings per share, using it to compute a trailingPEratio. Some analysts go even further and use expected earnings per share in the next financial year in the denominator and compute
a forwardPEratio. Earnings per share can also be computed before or after extraordinary items and based upon actual shares outstanding (primary)
or all shares that will be outstanding if managers exercise the options that they have been granted (fully diluted). In other
words, you should not be surprised to see different PE ratios reported for the same firm at the same point by different sources. In addition, you should be specific about your
definition of a PE ratio if you decide to construct an investment strategy that revolves around its value.

A Primer on Accounting Earnings

Before you look at whether the price-earnings ratio can be used as a measure of the cheapness of a stock, you do need to consider
how earnings are measured in financial statements. Accountants use the income statement to provide information about a firm's
operating activities over a specific period. In this section, you will examine the principles underlying earnings measurement
in accounting and the methods by which they are put into practice.

Two primary principles underlie the measurement of accounting earnings and profitability. The first is the principle of accrual accounting. In accrual accounting, the revenue from selling a good or service is recognized in the period in which the good is sold or
the service is performed (in whole or substantially). A corresponding effort is made on the expense side to match[1] expenses to revenues. This is in contrast to cash accounting, whereby revenues are recognized when payment is received and
expenses are recorded when they are paid. As a consequence, a firm may report high accrual earnings but its cash earnings
may be substantially lower (or even negative), or the reverse can apply.

The second principle is the categorization of expenses into operating, financing and capital expenses. Operating expenses are expenses that, at least in theory, provide benefits only for the current period; the cost of labor
and materials expended to create products that are sold in the current period is a good example. Financing expenses are expenses
arising from the nonequity financing used to raise capital for the business; the most common example is interest expenses.
Capital expenses are expenses that are expected to generate benefits over multiple periods; for instance, the cost of buying
land and buildings is treated as a capital expense.

Operating expenses are subtracted from revenues in the current period to arrive at a measure of operating earnings from the
firm. Financing expenses are subtracted from operating earnings to estimate earnings to equity investors or net income. Capital
expenses are written off over their useful life (in terms of generating benefits) as depreciation or amortization. Figure 3.1 breaks down a typical income statement.

While the principles governing the measurement of earnings are straightforward, firms do have discretion on a number of different
elements, such as the following:

Revenue recognition:
When firms sell products that generate revenues over multiple years, conservative firms spread revenues over time but aggressive
firms may show revenues in the initial year. Microsoft, for example, has had a history of being conservative in its recording
of revenues from its program updates (Windows 98, Windows 2000, etc.). On the other hand, telecommunication firms, in their
zeal to pump up revenue growth, in the late 1990s were often aggressive in recording revenues early.

Operating versus capital expenses:
Some expenses fall in a gray area between operating and capital expenses. Consider the expenses incurred by a cable company
to attract new subscribers. Companies that are more aggressive could legitimately argue that the benefits of these new subscribers
will be felt over many years and spread these expenses over time. At the same time, conservative companies will expense the
entire amount in the year in which the expense is incurred.

Depreciation and amortization:
While capital expenses are written off over time as depreciation or amortization charges, firms continue to have discretion
in how much and how quickly they depreciate assets, at least for reporting purposes. Here again, more aggressive firms can
report higher earnings by adopting depreciation and amortization schedules that result in smaller charges against earnings.

The bottom line, though, is that while the same accounting standards may apply to all firms, the fidelity to these standards
can vary across firms, making it difficult to compare earnings (and price-earnings ratios) across firms. If you are not careful,
you can very easily conclude that firms that are more aggressive in measuring earnings are cheaper than firms that are more
conservative. The problem gets worse when you are comparing the earnings of firms in different markets—Japan, Germany and
the United States, for example—with different accounting standards.

Determinants of PE Ratios

The simplest model for valuing a stock is to assume that the value of the stock is the present value of the expected future
dividends. Since equity in publicly traded firms could potentially last forever, this present value can be computed fairly
simply if you assume that the dividends paid by a firm will grow at a constant rate forever. In this model, which is called
the Gordon Growth Model, the value of equity can be written as:

The cost of equity is the rate of return that investors in the stock require, given its risk. As a simple example, consider
investing in stock in Consolidated Edison, the utility that serves much of New York city. The stock is expected to pay a dividend
of $2.20 per share next year (out of expected earnings per share of $3.30), the cost of equity for the firm is 8%, and the
expected growth rate in perpetuity is 3%. The value per share can be written as:

Generations of students in valuation classes have looked at this model and some of them have thrown up their hands in despair.
How, they wonder, can you value firms like Microsoft that do not pay dividends? And what you do when the expected growth rate
is higher than the cost of equity, rendering the value negative? There are simple answers to both questions. The first is
that a growth rate that can be maintained forever cannot be greater than the growth rate of the economy. Thus, an expected
growth rate that is 15% would be incompatible with this model; in fact, the expected growth rate has to be less than the 4%–5%
that even the most optimistic forecasters believe that the economy (U.S. or global) can grow at in the long term.[2] The second is that firms that are growing at these stable growth rates should have cash available to return to their stockholders;
most firms that pay no dividends do so because they have to reinvest in their businesses to generate high growth.

To get from this model for value to one for the price-earnings ratio, you will divide both sides of the equation by the expected
earnings per share next year. When you do, you obtain the discounted cash flow equation specifying the forward PE ratio for a stable growth firm.

To illustrate with Con Ed, using the numbers from the previous paragraph, you get the following:

Forward PE for Con Ed = ($2.20 / $3.30) / (.08 − .04) = 16.67

The PE ratio will increase as the expected growth rate increases; higher growth firms should have higher PE ratios, which makes intuitive sense. The PE ratio will be lower if the firm is a high-risk firm and has a high cost of equity. Finally, the PE ratio will increase as the payout ratio increases, for any given growth rate. In other words, firms that are more efficient
about generating growth (by earning a higher return on equity) will trade at higher multiples of earnings.

The price-earnings ratio for a high growth firm can also be related to fundamentals. When you work through the algebra, which
is more tedious than difficult, the variables that determine the price-earnings ratio remain the same: the risk of the company,
the expected growth rate and the payout ratio, with the only difference being that these variables have to be estimated separately
for each growth phase.[3] In the special case in which you expect a stock to grow at a high rate for the next few years and grow at a stable rate after
that, you would estimate the payout ratio, cost of equity and expected growth rate in the high growth period and the stable
growth period. This approach is general enough to be applied to any firm, even one that is not paying dividends right now

Looking at the determinants of price-earnings ratios, you can clearly see that a low price-earnings ratio, by itself, signifies
little. If you expect low growth in earnings (or even negative growth) and there is high risk in a firm's earnings, you should
pay a low multiple of earnings for the firm. For a firm to be undervalued, you need to get a mismatch: a low price-earnings
ratio without the stigma of high risk or poor growth. Later in this chapter, you will examine a portfolio of low PE stocks to see if you can separate the firms that have low PE ratios and are fairly valued or even overvalued from firms that have low PE ratios that may be attractive investments.